That's the mirror bumper, it softens the blow and cuts the noise as the mirror flips up.

Carefully remove it and then replace it with a new one. You can get it as part of a foam light seal repair kit for your camera; this also ensures that the sticky black goo which used to be foam and which prevents light from getting past the edges of the camera back gets replaced. Light seal kits are very cheap, and if you buy a pre-cut version then it makes a fiddly job a bit easier and potentially less messy. They're widely available on sites like ebay, just search for "k1000 light seals" and check that the kit includes a mirror bumper/buffer.

If you don't get it repaired the fuzz will get everywhere and can also get onto the film surface causing white spots on your photos or black spots on negatives/slides. The debris can also get into your lenses so remove it asap. Gooey foam light seals are even worse as it's both corrosive and abrasive (due to the grit it attracts) and gradually migrates to gum up the works. It can also result in light fogging on your photos (usually seen as red streaks from the top or bottom of the picture). Modern foam seals do not decompose like the old ones did.

I hope that I've helped you, please take a moment to rate my answer.